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s(105) ≤ 10.7893037837481588309268366600396176597363: exact contact refinement #568
Description
Credit name. PingYou Ltd — new contact refinement. Original construction and software credits are retained below.
Claim. s(105) ≤ 10.7893037837481588309268366600396176597363, rounded upward from the complete rational witness. Please register this improved upper bound.
The authoritative exact side is:
10789303783748158830926836660039617659736218711424421332884365754662904597598593330008796151/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Comparison. The preceding source certificate has side 10.789303783748158831034729697921. Its documented writer applies a 1+1e-20 dilation and rounds the side upward to 30 decimal places. If that side is C, its unpadded design lies in ((C-1e-30)/(1+1e-20), C/(1+1e-20)]. The submitted rational side lies strictly below the entire interval, by more than 4.29007519545e-29. Against the independently reconstructed unpadded source point, the decrease is about 4.35331025349e-29. Exact fractions and the source writer are retained in the package.
The original common-center contraction only removed certification padding and is not the result submitted here.
The public register, pending public reports, source repositories and retained comparisons were rechecked on 12 October 2026. This improves the strongest located bound for N=105.
Certificate. Please pin publication commit 260aaf50230483654802790589c2dfce73237604:
- Complete portable package
- Exact rational certificate
- Squares Project Witness/v2
- Method and replay instructions
- Native verification receipt
- Independent verification receipt
- Checksums
Exact certificate SHA-256: 8c684d15e87e772bec491f0c77db5b87c0246883875f5c0ad8b0c8a8ac8cd613.
Construction. Decode the pinned source centers and half-angle tangents. Use the guarded source as a seed for Evan Daniel's original solver at 77f3c0ab479b9a787478ccc8dae378df219f85ea: project onto the inherited contact system, then close it with 32 selected translation coordinates frozen. The same 435 corner/edge and wall equations occur in the new result and the inverse-dilation source control. Active angles follow from those equations; free-square orientations are inherited. No angle sweep or random perturbation is used.
The source control, when passed back through the documented old writer, exactly reproduces the old side and every one of its 97 nonfree square rows. The new metric realization was reproduced at 100, 120 and 140 digits; the final exact witness uses the 140-digit result with a 1e-80 rational-certification guard. Full physical-square coordinates, contact indices and reproduction instructions are included.
Checking. Extract the package, enter n105-squares-project, and run python3 -B VERIFY.py with Python 3.10+ (without -O). Exact separating-axis and rational polygon-intersection implementations verify all 105 unit squares, 420 wall conditions and 5,460 unordered pairs. Deliberately duplicated and out-of-container squares are rejected. Exact native conversion preserves every corner. Both unchanged Squares Project native verifiers at 074ac28d4ceb9a1897303f936d794771cfc6a7bd accept the witness. Separate implementations share the same rational input; these are computational checks, not independent human audits.
Scope. The N105 solver has a nonzero residual in frozen translation directions, so no stationarity or local-optimality claim is made. The result establishes exact feasibility and strict improvement; no global-optimality or lower-bound claim is made. Maintainer acceptance is a separate step.
Lineage and credit. Ryan Xu: original layout; Francisco Couzo: preceding refinement; Evan Daniel: contact solver; PingYou Ltd: this new contact refinement and submission. The immediate input is the pinned source certificate. Please retain this lineage and credit the new refinement to PingYou Ltd. Upstream software/schema licenses are retained.
AI assistance. Computation, checking and submission preparation were AI-assisted; the requested attribution is as stated above.
Activity
jlevy commentedon Oct 14, 2026
@BuddenPing, thank you. We have the n105 contact refinement from #568, pinned at 260aaf5 (n105.cert.json, SHA-256 8c684d15…). We retain it as derived exact facts. It replayed and passed both of this project's maintained exact checkers, and both refused the two controls. Its side is 1.079e-19 below the current register entry at 105, Francisco Couzo's certificate, a difference at the scale of that certificate's padding. A review comes next, and it will say how the record treats such a difference before anything is registered. PR #574 states a further n105 certificate; it is a separate import.
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jlevy commentedon Oct 14, 2026
@BuddenPing, thank you; this is the report-order evaluation of every open report at the counts #568 claims.
At each count, a report is recorded when its side is decidably below every side reported before it (and below the record on main); a tie stays with the earlier report. Sides are rounded up at 12 places.
The registrations are in the records pull request #602, and a follow-up with the result ids and rungs will come once it is on main.
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jlevy commentedon Oct 14, 2026
@BuddenPing, thank you. With #602 merged, your n105 contact refinement is registered on
main:A correction to our reply of 14 October, which said a review would settle how the record treats a 1e-19 difference before anything was registered: the per-count ledger registers it now, as a regularization of the packing it tightens, and the review follows.
Evidence:
E-pingyou-568-certificate-report(your report, recorded). Onmain: RESULTS.md, the packet.Generated by Claude Code
requests: record #602's post-merge follow-ups and the 14 October verd…
intake: retain and replay PingYou Ltd's seven certificates of 12 October
jlevy commentedon Oct 15, 2026
@BuddenPing, thank you. Where this request stands in the record on
main.Corrections to earlier replies.
What is registered.
On the case page. Our reply of 14 October said adoption would follow the review. On 15 October 2026 T-170 became the house at 105; Ryan Xu's packing as Francisco Couzo improved it (T-130) stays retained as history.
On
main.packing/frontier/RESULTS.md,docs/project/reviews/review-2026-10-14-upper-bound-imports-561-593.md,packing/frontier/n-105.md.Nothing you asked for is queued, so this issue is closed with this comment.
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